Two related topics that tend to cause incomprehension between mostly liberal Europeans and not as liberal Americans are abortion and capital punishment. Generally speaking the former group are in favour abortion and against capital punishment while Americans on the whole are perceived as holding the opposite view. The problem is that there are in fact four possible options not two and cases can be made for each.
There are wild exaggerations on all sides in these arguments as proponants of one view attempt to demonise their opponents, in this discussion we will assume that those in favour of abortion and/or capital punishment want it to be an occasional thing not the standard treatment/punishment and that those against abortion are willing to permit it in those cases where the pregnancy is likely to kill the mother if it proceeds. With that noted lets see how the four different choices stack up in terms of morality and logic.
1) Oppose both capital punishment and abortion rights
What one might call the Catholic position. If you believe that (human) life is sacred and that ending a life or potential life for any reason is therefore a major sin then this is the only possible position. The key here is that you believe that humans have a right to life simply from that fact and that therefore any life is better than no life. This is logically consistent and fits in nicely with much religious idealism. I don't agree with this position but I find it defensible.
2) Oppose capital punishment but support abortion rights
The Euroliberal position. The Euroliberal position arises from a combination of a belief in the rights of women combined with the idealism of the "life is sacred" viewpoint. The key point here is that you believe that humans have a right to life simply by being born but that sometime before birth they are not alive and therefore do not count. The problem is that, IMO, this position is logically indefensible as you end up killing innocents and not killing monstrous murderers who have themselves killed.
3) Support capital punishment but oppose abortion rights
The Religious Fundamentalist position. This is effectively a position that believes in protecting the innocent but removing the worst of humankind from the earth. What this says is the reverse of the Euroliberal one - that every potential life has the right to come into existance but that a human can forfeit his or her right to life by certain actions. This viewpoint seems to be held by both Christian Fundamentalists and by Islamic ones. I consider this to be the logically defensible but again I disagree with it.
4) Support both capital punishment and abortion rights
The pragmatic or darwinist viewpoint. Effectively this viewpoint says the reverse of the Catholic viewpoint - namely that in fact no life may be preferable to a bad life and that you have no guaranteed right to continued life. Another way to look at this viewpoint is that it is the "nature red in tooth claw" approach where the genepool is culled of those who are undesirable. With respect to the death penalty the culling is direct, with respect to abortion it means that the next generation is better. Logically this is also defensible and it is the position I agree with.
Political parties and their viewpoints
Unfortunately in (Western) Europe no mainstream political party supports either position 3 or 4 despite considerable evidence that voters in Europe are in fact in favour of the death penalty. Also except for Catholic groups very few political organizations support option 1 thus option 2, the one that I consider to be the most logically flawed is the one that wins be default.
In the US on the other hand the position is more complicated. The Republicans are generally a mixture of 3 and 4 while the Democrats are a mixture of 2 and 4, however there is considerable overlap and I supect you could find members of both parties that hold any one of the four possible options. UPDATE Perhaps I should clarify what I mean when I say I support the death penalty and abortion: I think it was President Clinton who said abortion should be "safe, legal and rare". That description pretty much covers my feelings, abortion needs to be an option in those cases where there are no good choices just a selection of bad ones.
As with abortion I want capital punishment to be "safe, legal and rare" where "safe" means safe from being a mistaken conviction. Essentially I see the death penalty being used only for those cases where the criminal is caught literally red-handed or where the evidence is otherwise incontrovertable. In addition I would tend to want to limit it to cases where the murderer has killed or attempted to kill more than once. A serial killer or someone who goes "postal" for example.